Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe

Simulations with different lattice Dirac operators for valence and sea quarks

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a "mixed" action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to O(a), and the appropriate low energy chiral effective Lagrangian is constructed, including the leading O(a) contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.Comment: 17 pages, 1 ps figure (2 clarification paragraphs added

Asymptotic behavior of age-structured and delayed Lotka-Volterra models

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov functional that enables us to reduce the attractive set to either the nontrivial equilibrium or to a periodic solution. We then prove the asymptotic stability of the nontrivial equilibrium where, depending on the existence of the periodic trajectory, we make explicit the basin of attraction of the equilibrium. Finally, we prove that these results can be extended to the initial PDE problem.Comment: 29 page

A mathematical model for mechanotransduction at the early steps of suture formation

Growth and patterning of craniofacial sutures are subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron x-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (\emph{Polypterus bichir}) and a placoderm (\emph{Compagopiscis croucheri}), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion

Chiral Perturbation Theory for the Quenched Approximation of QCD

[This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_\pi$, $m_\pi$, $m_K$, and the ratio of $\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.Comment: 14 page

Statistical Arbitrage Mining for Display Advertising

We study and formulate arbitrage in display advertising. Real-Time Bidding (RTB) mimics stock spot exchanges and utilises computers to algorithmically buy display ads per impression via a real-time auction. Despite the new automation, the ad markets are still informationally inefficient due to the heavily fragmented marketplaces. Two display impressions with similar or identical effectiveness (e.g., measured by conversion or click-through rates for a targeted audience) may sell for quite different prices at different market segments or pricing schemes. In this paper, we propose a novel data mining paradigm called Statistical Arbitrage Mining (SAM) focusing on mining and exploiting price discrepancies between two pricing schemes. In essence, our SAMer is a meta-bidder that hedges advertisers' risk between CPA (cost per action)-based campaigns and CPM (cost per mille impressions)-based ad inventories; it statistically assesses the potential profit and cost for an incoming CPM bid request against a portfolio of CPA campaigns based on the estimated conversion rate, bid landscape and other statistics learned from historical data. In SAM, (i) functional optimisation is utilised to seek for optimal bidding to maximise the expected arbitrage net profit, and (ii) a portfolio-based risk management solution is leveraged to reallocate bid volume and budget across the set of campaigns to make a risk and return trade-off. We propose to jointly optimise both components in an EM fashion with high efficiency to help the meta-bidder successfully catch the transient statistical arbitrage opportunities in RTB. Both the offline experiments on a real-world large-scale dataset and online A/B tests on a commercial platform demonstrate the effectiveness of our proposed solution in exploiting arbitrage in various model settings and market environments.Comment: In the proceedings of the 21st ACM SIGKDD international conference on Knowledge discovery and data mining (KDD 2015

Multiscaled Cross-Correlation Dynamics in Financial Time-Series

The cross correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform to calculate correlation matrices over different timescales and then explore the eigenvalue spectrum over sliding time windows. The dynamics of the eigenvalue spectrum at different times and scales provides insight into the interactions between the numerous constituents involved. Eigenvalue dynamics are examined for both medium and high-frequency equity returns, with the associated correlation structure shown to be dependent on both time and scale. Additionally, the Epps effect is established using this multivariate method and analyzed at longer scales than previously studied. A partition of the eigenvalue time-series demonstrates, at very short scales, the emergence of negative returns when the largest eigenvalue is greatest. Finally, a portfolio optimization shows the importance of timescale information in the context of risk management

Changes in the prevalence and correlates of weight-control behaviors and weight perception in adolescents in the UK, 1986 to 2015

Importance: In the context of the growing prevalence of childhood obesity, behaviors aimed at weight loss and their psychological burden might be increasing. Objective: To investigate whether the prevalence of weight-control behaviors and weight perception, including their association with depressive symptoms, has changed in the 3 decades between 1986 and 2015. Design, Setting, and Participants: This study used data from repeated cross-sections from successive longitudinal birth cohort studies. These included general population samples of UK adolescents aged 14 to 16 years from 3 ongoing birth cohorts: the British Cohort Study 1970 (children born between April 5 and 11, 1970; data collected in 1986), the Avon Longitudinal Study of Parents and Children (mothers with expected delivery between April 1, 1991, and December 21, 1992; data collected in 2005), and the Millennium Cohort Study (children born between September 1, 2000, and January 11, 2002; data collected in 2015). A total of 22 503 adolescents with data available on at least 1 weight-control or weight-perception variable in midadolescence were included in the study. Data were analyzed from August 1, 2019, to January 15, 2020. Main Outcomes and Measures: Self-reported lifetime dieting and exercise for weight loss, current intentions about weight (doing nothing, lose weight, stay the same, gain weight), and weight perception (underweight, about the right weight, overweight) adjusted for body mass index. The secondary outcome was depressive symptoms. Exposures: The main exposure was time (ie, cohort); secondary exposures were weight-change behaviors and weight perception. Results: The study cohort included 22 503 adolescents (mean [SD] age, 14.8 [0.3] years; 12 061 girls [53.6%]; and 19 942 White individuals [89.9%]). A total of 5878 participants were from the British Cohort Study, 5832 were from the Avon Longitudinal Study of Parents and Children, and 10 793 were from the Millennium Cohort Study. In 2015, 4809 participants (44.4%) had dieted and 6514 (60.5%) had exercised to lose weight compared with 1952 (37.7%) and 344 (6.8%) in 1986. Furthermore, 4539 (42.2%) were trying to lose weight in 2015 compared with 1767 (28.6%) in 2005. Although girls were more likely to report these behaviors in all years, their prevalence increased more in boys over time (lifetime dieting in boys: odds ratio [OR], 1.79; 95% CI, 1.24-2.59; in girls: OR, 1.23; 95% CI, 0.91-1.66; currently trying to lose weight in boys: OR, 2.75; 95% CI, 2.38-3.19; in girls: OR, 1.70; 95% CI, 1.50-1.92). Adolescents also became more likely to overestimate their weight (boys describing themselves as overweight adjusting for body mass index, 2005 vs 1985 OR, 1.60; 95% CI, 1.17-2.19; 2015 vs 1985 OR, 1.36; 95% CI, 1.04-1.80; girls describing themselves as underweight, after adjusting for body mass index, 2015 vs 1986 OR, 0.51; 95% CI, 0.28-0.91). Girls who described themselves as overweight experienced increasingly greater depressive symptoms over time compared to girls who described their weight as about right (mean difference 1986, 0.32; 95% CI, 0.22-0.41; mean difference 2005, 0.33; 95% CI, 0.24-0.42; mean difference 2015, 0.56; 95% CI, 0.49-0.62). Conclusions and Relevance: These findings suggest that the growing focus on obesity prevention might have had unintended consequences related to weight-control behaviors and poor mental health. Public health campaigns addressing obesity should include prevention of disordered eating behaviors and be sensitive to negative impact on mental health

B --> pi and B --> K transitions in partially quenched chiral perturbation theory

We study the properties of the B-->pi and B-->K transition form factors in partially quenched QCD by using the approach of partially quenched chiral perturbation theory combined with the static heavy quark limit. We show that the form factors change almost linearly when varying the value of the sea quark mass, whereas the dependence on the valence quark mass contains both the standard and chirally divergent (quenched) logarithms. A simple strategy for the chiral extrapolations in the lattice studies with Nsea=2 is suggested. It consists of the linear extrapolations from the realistically accessible quark masses, first in the sea and then in the valence quark mass. From the present approach, we estimate the uncertainty induced by such extrapolations to be within 5%.Comment: Published versio

Lattice QCD with Ginsparg-Wilson fermions

Lattice QCD using fermions whose Dirac operator obeys the Ginsparg-Wilson relation, is perhaps the best known formulation of QCD with a finite cutoff. It reproduces all the low energy QCD phenomenology associated with chiral symmetry at finite lattice spacings. In particular it explains the origin of massless pions due to spontaneous chiral symmetry breaking and leads to new ways to approach the U(1) problem on the lattice. Here we show these results in the path integral formulation and derive for the first time in lattice QCD a known formal continuum relation between the chiral condensate and the topological susceptibility. This relation leads to predictions for the critical behavior of the topological susceptibility near the phase transition and can now be checked in Monte-Carlo simulations even at finite lattice spacings.Comment: 6 pages, REVTEX. Added a new section on the critical behavior of the zero modes near T_c with various flavors. This version will appear in Phys. Rev.